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Variational Iteration Techniques for Solving Boundary Value Problems

Thesis Info

Access Option

External Link

Author

Mohyud-Din, Tauseef

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2009

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/297

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727658019

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This work is devoted to the study of variational iteration technique and its modifications for the solution of initial and boundary value problems. The proposed modifications are made by the elegant coupling of He’s polynomials and Adomian’s polynomials in the correction functional of variational iteration method. The proposed techniques are applied without any discretization, linearization and unrealistic assumptions. It has been observed that variational iteration method and its modified versions are very efficient and reliable for the solution of nonlinear problems of physical nature. Several examples are given which reveal the efficiency and accuracy of the suggested algorithms.
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چوتھا باب: کتب مقدسہ

تنخ

باب چہارم کے اہم نکات

  1. یہودی کتب مقدسہ کا تعارف۔
  2. مصنفہ و زبانی قانون میں فرق۔
  3. عبرانی بائیبل اور اس کے تراجم کا تعارف، تاریخ اور اہمیت۔
  4. مشنا، جیمارا ور تلمود کا تعارف۔
  5. ہلاخا کی تاریخ و اہمیت۔
  6. اپاکرفا، مدراش، زوہر اور سیدور کا تعارف۔

 

مذہبی یہودی اس بات پر یقین رکھتے ہیں کہ ان کی رہنمائی کے لیے خدا نے متعدد کتابیں نازل کیں۔ یہ کتب خدا کے الفاظ ہیں جو مختلف ادوار میں مختلف انبیا و رسل پر نازل ہوئے۔ چنانچہ وہ ان کتب کو یہودی مذہب کی بنیاد مانتے ہیں۔ یہودیوں کے تمام فرقے ان کتب کی عزت کرتے ہیں، تاہم معنی اخذ کرنے اور تشریحات میں دیگر مذاہب کے پیروکاروں کی طرح ان میں بھی اختلاف پایا جاتا ہے جو مذہبی نقطہ نظر سے کافی اہمیت کا حامل ہے

 

 دریائے نیل کے کنارے اگنے والے نرسل کی طرح کے پودے سے بنائے گئے کاغذ جسے پیپرس/پپائرس/قرطاس مصری کہا جاتا ہے یا جانوروں کی چمڑی سے بنے کاغذ پر انہیں مختلف ادوار میں مختلف لوگوں نے لکھا۔ ہاتھ سے لکھی جانے والی ان کتب میں کاتبین نئے مشمولات بھی شامل کرتے رہے، مثلاً "کتابِ یسعیاہ" چونکہ تین مختلف ادوار سے متعلق ہے اس لیے کہا جاتا ہے کہ اسے تین مختلف لوگوں نے لکھا ہے۔ زیادہ تر محققین کا خیال ہے کہ تقریبا 400 قبل مسیح تک ان کتب کی تکمیل ہوتی رہی ہے۔[1] ان میں سے بیشتر کتب کی زبان عبرانی ہے جبکہ کچھ کتابیں آرامی زبان میں بھی لکھی گئیں ہیں۔ آرامی ذخیرہ الفاظ میں عبرانی سے ملتی جلتی ہے لیکن گرائمر اور لغوی اعتبار سے مختلف ہے۔۔ جلاوطنی سے پہلے تک یہ کتب...

قرآنی معاشرتی احکام اور لفظ لعلکم: حکم و عصری اطلاقات

In the Holy Quran, Allah has mentioned many such social rules that are very important for the peace & stability of a society and welfare of human beings. This article will not only highlight the word “La'allakum” in terms of meaning, diction and eloquence but also explain its usage for different purposes. Apart from this, in this article light will be thrown on such social rules that have been defined under the word “La'allakum" along with its philosophy and their implementations in the present era.

Water Demand Management and Economic Value of Water in the Indus Basin

The present study was conducted on Water Demand Management and Economic Value of Water in the Indus Basin. To fulfill the objective of the study secondary and primary data sets were used. The primary data for study was collected through a farm survey of nearly 120 farmers on distributaries in Sargodha district. The data for supply and demand was taken from secondary sources. The sources include but not limited to the Agricultural Statistics of Pakistan, 2005-06, Economic Survey, 2006, the Water and Power Development Authority. The crop yield stress data was taken from Mona Reclamation project and Punjab Agriculture Research Institute, Faisalabad. Water supply and demand was estimated by using water balance equations. In order to calculate the Economic Value of Irrigation Water residual imputation approach was used. The change in net income method can be adapted to mathematical programming models (LP model) of farm situations to approximate a functional relationship between net benefits and irrigation water use . The study found that the water balance was 140 billion M3 including availability of rainfall. There was a net recharge to groundwater of the Indus Basin in the order of 63 billion M3, which can be pumped for consumptive and non-consumptive uses. The gross water supply for the agriculture sector was nearly 190 billion M3 from both surface and groundwater resources. The gross water demand for the agriculture sector was nearly 210 billion M3. Thus, there was a shortfall of around 20 billion M3 for the sector. In all four Linear Programming models were developed for small, large, head and tail farmers in the Sargodha region. The average size of small holding was 6.5 acres and that of large was 32 acres, while head farm size was 15 acres and that tail 13 acres. The cropping intensities at small, large, head and tail were 135 percent, 116 percent, and 151 percent and 127 percent, respectively. The analysis of cropping pattern showed that wheat was the predominant crops at all farms followed by Kharif and Rabi fodders. However, most of the farmers showed mixed cropping pattern citrus with wheat and citrus with berseem. The results revealed that economic value of water at discounted water availability varied from Rs.1.63 per M3 to Rs 3.23 per M3 on small farm. The economic value of water was Rs 1.63/ M3 even at 60 percent water discount. In case of large farm, the economic value varied from Rs.1.93 per M3 to Rs 3.76 per M3 at various discount scenarios. Even under extreme stress scenarios, the economic value was Rs 1.93/ M3. In case of head, the value varied from Rs. 1.03/ M3 to Rs. 2.01/ M3 and at the tail farm it varied from Rs. 1.39/ M3 to Rs 2.74/ M3. The analysis showed that farmers have the paying capacity of water charges under extreme water stress scenarios. It is implied that water pricing policies, as a strategy for water demand management, aims at water conservation and consequently increase in agricultural production. It is anticipated that irrigation water efficiency will be improved, as farmers change their strategy and practices in irrigated agriculture.